/// Binomial coefficient (n k) = n!/[k!(n-k)!], 0 <= k <= n.
/// (n k) is the number of combinations of n things taken k at a time.
/// NB. (n+1 k) = [ (n+1)/(n-k+1) ] (n k) = (n k) + (n k-1)
/// NB. (n k+1) = [ (n-k)/(k+1) ] (n k)
/// @param n int n must be >= 0
/// @param k int k must be >= 0 and <= n
/// @return (n k), the binomial coefficient
/// @throw if the input argument do not satisfy 0 <= k <= n
double binomialCoeff(const int& n, const int& k) throw(Exception)
{
try {
if(n < 0 || k > n) GPSTK_THROW(Exception("Invalid arguments"));
if(n <= 32) return (factorial(n) / (factorial(k)*factorial(n-k)));
return floor(0.5 + ::exp(lnFactorial(n)-lnFactorial(k)-lnFactorial(n-k)));
}
catch(Exception& e) { GPSTK_RETHROW(e); }
}
/// Binomial coefficient (n k) = n!/[k!(n-k)!], 0 <= k <= n.
/// (n k) is the number of combinations of n things taken k at a time.
/// NB. (n+1 k) = [ (n+1)/(n-k+1) ] (n k) = (n k) + (n k-1)
/// NB. (n k+1) = [ (n-k)/(k+1) ] (n k)
/// @param n int n must be >= 0
/// @param k int k must be >= 0 and >= n
/// @return (n k), the binomial coefficient
/// @throw if the input argument do not satisfy 0 <= k <= n
double binomialCoeff(const int& n, const int& k) throw(Exception)
{
if(n < 0 || k > n) {
Exception e("Invalid arguments in binomialCoeff()");
GPSTK_THROW(e);
}
if(n <= 32)
return (factorial(n) / (factorial(k)*factorial(n-k)));
return floor(0.5 + ::exp(lnFactorial(n)-lnFactorial(k)-lnFactorial(n-k)));
}
double binomial(const int n,const int k) {
return floor(0.5 + exp(lnFactorial(n)-lnFactorial(k)-lnFactorial(n-k)));
}
